Control method for an extra high voltage d-c transmission connecting two three-phase networks

ABSTRACT

Simultaneous power and voltage control by a d-c-tie between a-c networks is carried out by means of fixed and switchable inductive and capacitive compensation elements including the tap changer of both converter transformers of a d-c-tie for setting the optimum operating point by a transformation ratio of the converter transformer taps matching the primary current ratio, of the converter transformer taps for the maximally permissible stage of the one converter transformer, taking into consideration control, extinction and overlap angles of the d-c-tie.

BACKGROUND OF THE INVENTION

The present invention relates to a combined control method for a d-c-tie connecting two independent three-phase a-c networks.

In known control methods for a d-c-tie, the active power of the system is controlled and the reactive power is adapted to the reactive power demand of the respective a-c network with the aid of shunt reactors or capacitors, static compensators (for instance, thyristor-controlled reactors or capacitors) and/or synchronous condensors. For the controlled compensation devices for both a-c networks, a considerable amount of means is required for a necessary fine-step or stepless voltage adaptation to the active power to be transmitted. In addition, it is possible to switch the tap changer of the converter transformer in the wrong direction before the control arrangement can ascertain that compensating devices must be switched, so that the tap position must be switched back in the direction of its starting position after the respective compensation device has been switched by it independently; switching beyond its starting position may even become necessary. The control process with successive switching actions of the tap changer allows only a slow control; the required active and reactive power cannot be maintained during switching operations which take a relatively long time. In addition, the tap changer is stressed unnecessarily by the back and forth stepping operations.

In order not be extend the control time further, only the side of the d-c-tie connected to the weaker a-c network is frequently controlled in the sense of meeting the predetermined reactive power conditions of this a-c network, and the other side of the d-c-tie associated with the stronger a-c network is made to approach, as far as reactive power is concerned, the demand only via switchable shunt reactors or capacitors as compensating elements, so that in the second a-c network, the reactive power required there cannot be maintained exactly. This method further cannot recognize a control into undesirable boundary regions so that in the event of changes of the desired power or in the case of voltage changes in the a-c networks, no sufficient control reserve is provided. If in the case of two weak a-c networks an exact control is required also on the side of the second a-c network a further slowing-down of the control is resulted.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a substantially faster control for both a-c sides of the d-c-tie and to determine an operating point which makes it possible to maintain the predetermined reactive power condition for both a-c networks and which, in the case of dynamic processes related to changes, of active power in the d-c-tie allows the fast determination of a new operating point which allows on both a-c sides of the d-c-tie the smallest possible deviations from the respective set-point values of the a-c network voltages and reactive power of the a-c networks, where switchable shunt reactors or capacitors suffice.

The above and other objects of the present invention are achieved by a control method for a d-c-tie (high-voltage transmission system) connecting two a-c networks with active power control and combined reactive-power influencing by shunt reactors or shunt capacitors and converter transformers with tap changers for maintaining the voltage of the a-c networks. Simultaneous active and reactive power control of both a-c networks is performed by combinations of fixed and switchable shunt capacitors and/or shunt reactors, including the tap position of both converter transformers for setting the optimum operating point at the maximally permissible tap position for the respective operating voltage of the one converter transformer, wherein the ratio of the primary currents of the two converter transformers and the ratio of the maximally permissible tap position of the one converter transformer to a fitting tap position of the other converter transformer is chosen in accordance with the relationship ##EQU1## taking into consideration the dependence of the prevailing d-c current ##EQU2## in the direction of obtaining a permissible transmission current I_(dmin) meeting all network requirements, equal to one-half of the sum of the d-c currents of the two converters, wherein u₁, u₂ are the transformation ratios of the respective tap position; S_(iV1), S_(iV2) are the a-c side currents of the converter transformers; b is the number of the series-connected rectifier bridges; ρ₁, ρ₂, χ₂, χ₁ are variables dependent on control angles α, extinction angles γ, and overlap angles u in accordance with the following equations: ##EQU3##

The control method according to the invention starts out from the reactive-power demand of both a-c networks, the a-c network voltage required in each case as well as the required transmission power of the d-c-tie system, while these values are adapted to the actual network conditions. From the permissible voltage range and the fixed and switchable shunt reactors or capacitors provided as well as the converter transformer tap positions and the required voltage-dependent reactive power of each a-c network, a region is obtained in a reactive power, active power diagram for operating of the converters, within which operating points are determined in steady-stage operation which meet all a-c network conditions. Adding and disconnecting capacitive or inductive compensation elements takes place if the range is exceeded or not reached. In the case of dynamic processes, the operating point may lie outside of the mentioned range.

For supporting a a-c network, the d-c current can be adjusted as the transmission current determined for the side of the d-c-tie assigned to this a-c network. The reactive power of the other a-c network then deviates from the set value accordingly more.

If the compensation elements are designed sufficiently large, the reactive power of one or both converters are changed in the direction of an approximation by switching of shunt capacitors or reactors, the position of the transformer tap changer assigned to them exhibits the smallest possible difference. Finally, the tap positions for each converter transformer as well as the d-c currents of the converters are determined by the given network data and the operating data and preferably the smallest possible common d-c current is determined therefrom which is sufficient for meeting all conditions of both a-c networks.

After coarse adjustment by the compensation elements, the optimum operating point is advantageously determined by addressing the combination of the tap position determined in accordance with the method of the invention, so that fine tuning by a static compensator or a synchronous condenser is not necessary.

The method of the invention makes possible

(a) a targeted addressing of an unambiguous operating point which meets all network requirements,

(b) the statement of missing or not required compensating elements in case of structural changes of the a-c networks with changes of the reactive power required by them,

(c) the determination of another favorable operating point in the event of a failure or disconnecting of compensating elements for servicing purposes, as well as

(d) the adjustment of the most favorable operating point during occurring power or voltage changes (dynamic processes) during the time interval in which no compensation elements and no tap changer can yet operate.

BRIEF DESCRIPTION OF THE DRAWINGS

Further details will be explained with the aid of an example for a d-c-tie operating in accordance with the control method of the invention, with reference to the drawings, in which:

FIG. 1 shows a d-c-tie back to back coupling connecting two a-c networks schematically with fixed filter circuits and switchable compensation elements;

FIG. 2 shows an active-reactive power diagram for the d-c-tie with a range of value pairs in which the d-c-tie operates for meeting all operating conditions and specifically as a function of the control or the extinction angle and of the transmitted d-c current and of the transformer tap and a nominal voltage of 230 kV;

FIG. 3 shows another embodiment of a d-c-tie connecting two a-c networks; and

FIG. 4 are graphs explaining the operation of the d-c-tie of FIG. 3 with voltage conditions of the a-c network N1.

DETAILED DESCRIPTION

The operating data associated with the a-c networks N1 and N2 are designated with appropriate subscripts and furthermore with additional subscripts N and n, of which the subscript N indicates network variables and the subscript n indicates nominal values.

In the following description, the following designations are made: ##EQU4##

For the example shown in the following of d-c-tie with nominal active power P_(n) =200 MW, P_(ref) =20 MW and a nominal network voltage U_(Nn) =230 kV, the requirements for the a-c networks N1 and N2 given by the utility are as follows:

    ______________________________________                                         Q.sub.N1                                                                             = 33 MVAr (capacitive)                                                   Q.sub.N2                                                                             = 40 MVAr (capacitive)                                                   U.sub.N1                                                                             = 241.5 kV corresponding to 241.5/230 = 1.05 per unit                    U.sub.N2                                                                             = 234.6 kV corresponding to 234.6/230 = 1.02 per unit                    ______________________________________                                    

From this, the necessary compensation elements keeping in mind the filter circuits FK can be calculated with the values preferably intended for filtering harmonics:

FK₁ ≡Q_(FK1) =105 MVAr; in addition, a shunt capacitor C₁ ≡Q_(cap1) =35 MVAr

FK₂ ≡Q_(FK2) =105 MVAr: additionally a shunt capacitor C₂ ≡Q_(cap2) =35 MVAr

For this transmission in the range from full to partial loads, with the available compensation elements, the transformer data for the converter transformers as well as the voltage-dependent reactive power requirements of the a-c networks, there is determined an operating range of the converter reactive power between 90 and 155 MVAr, which assures reliable operation for all operating requirements and which has sufficient control reserves in both power flow directions for dynamic processes.

The following is obtained for:

Network N1

Reactive power demand Q_(N1) =33.0 MVAr (capacitive) for U_(N1) =241.5 kV; (1.05 p.u.)

Filter circuit FK₁ with Q_(FK1) =105×1.05² =115.76 MVAr

C₁ with Q_(cap1) =35×1.05² =38.59 MVAr

no shunt reactors required, i.e., Q_(ind1) =0

Network N2

Reactive power demand Q_(N2) =40.0 MVAr (capacitive) for U_(N2) 234.6 kV; (1.02 p.u.)

Filter circuit FK₂ with Q_(FK2) =105×1.02² =109.24 MVAr

C₂ with Q_(cap2) =35×1.02² =36.41 MVAr

no shunt reactors necessary, i.e., Q_(ind2) =0

From this is obtained:

    Q.sub.V1 =Q.sub.FK1 +Q.sub.N1 +Q.sub.cap1 -Q.sub.ind1 =115.76-33.0+38.59-0=121.35 MVAr

    Q.sub.V2 =Q.sub.FK2 +Q.sub.N2 +Q.sub.cap2 -Q.sub.ind2 =109.24-40.0+36.41-0=105.66 MVAr

The calculated reactive power of the converters Q_(V1) =121.35 MVAr and Q_(V2) =105.66 MVAr are in the said operating range between 90 and 155 MVAr.

With the a-c network conditions given by the utility, the active power at the inverter and the required compensation elements for this example, the tap position for each converter transformer of the d-c-tie and the transmission current I_(dmin) can be determined in the following manner from ##EQU5## φ is set equal to α and γ, respectively, in first approximation: ##EQU6## (with b=number of converter bridges connected in series).

If concrete values are substituted, the following is obtained:

    ______________________________________                                         cos ρ.sub.1 = 0.1626 and thus                                                                 ρ.sub.1 = 80.64°                                                    ρ.sub.2 = 79.28°                                 s.sub.ivl = 0.2940 kA and                                                                         S.sub.iV2 = 0.2646 kA                                       u.sub.1 = 9.20° and                                                                        u.sub.2 = 9.23°                                      ε.sub.1 = 0.08 and                                                                        ε.sub.2 = 0.08                                      ρ.sub.1 = 0.0835 and                                                                          ρ.sub.2 = 0.1060                                         .sub.1 = 0.9954 and                                                                               .sub.2 = 0.9933                                            ______________________________________                                    

From the relationship according to the idea of the invention, I_(d1) =I_(d2), the relationship of the transformation ratios ##EQU7## can be calculated as 0.9.

Accordingly, the transformation ratio u₂ of the converter transformer associated with the a-c network N2 is 0.9-times as large as the transformation ratio u₁ of the converter transformer associated with the network N1, and the possible tap combinations are fixed thereby.

In the numerical example, both converter transformers are equal and each have 35 taps. For calculating the smallest permissible d-c current I_(dmin) it is assumed that one of the two converter transformers is always set to the highest tap permissible for this a-c network voltage, in the case of the tap 35 of the converter transformer T1 of the a-c network N1, since u₂ is smaller than u₁.

At the converter transformer T2 associated with the a-c network N2, the tap coming closest to the calculated value u₂ =u₁(35) ×0.9 is set.

For an actual value u₁(35) =0.110444, a numerical value of u₂ =0.09939 is obtained.

This is approached closest by the tap 28 of the second converter transformer T2 with u₂(28) =0.09924.

The d-c current for the 35th and 28th tap calculated therefrom is obtained as ##EQU8## is thus obtained with 1.7107 kA as the smallest possible direct current for meeting all specified network conditions and within the operation range of the converters.

For minimal deviations from the required data of both sides, also other tap ratios such as 34/37, 33/26 or 32/25 can be used, where I_(dmin) has an increasingly larger magnitude. In this connection it must be noted that the current I_(dmin) which increases with decreasing tap combinations must increase only to such an extent that it does not exceed the given nominal value I_(dn) or the control angle α, the extinction angle γ, and the overlap angle u stay within their permissible limits.

For acceptable operation of the d-c-tie, meeting the specified conditions, it must be assumed that I_(dmin) can flow in connection with the permissible tap position, where smaller deviations of the set-point values for the active and reactive power can possibly be corrected by the control or extinction angle.

The control method according to the invention can proceed in an analog as well as a digital manner and allows, as explained, the determination of the optimum operating point for steady-state operating cases as well as of the operating point with the lowest deviation from the desired values for both networks in case of dynamic processes in the networks.

An application of the invention is possible in the manner described in the following not only for two given a-c networks N1 and N2 coupled by the d-c-tie according to FIG. 1, but also for the cooperation of a-c networks of which at least the one a-c network can have different stages of development and the requirement is to be met that the converter transformers, the reactive power control for the d-c-tie and the determined compensation elements are sufficient for all a-c network configurations.

As an example in FIG. 3, the a-c network N1 is to remain unchanged and the a-c network N2 is to be developed in stages to become the network N2a and finally, in a further stage, the network N2b.

Each a-c network is connected according to FIG. 3, similar as in FIG. 1, permanently as a not switchable filter circuit FK1 and FK2 for the elimination of harmonics.

By the utility, network voltage limits permitted for each of the a-c networks N1, N2, N2a and N2b for active power P_(ref) and P_(n) in the two directions of power flow within voltage ranges A for steady-state operation and ranges B permitted only for dynamic processes according to FIG. 4 are set as well as the corresponding reactive powers Q_(N) according to Tables Ia to IVa. From these Tables Ia to IVa, maximum and minimum inductive and capacitive reactive-power demand of a-c networks are given.

In addition, the average values for inductive or capacitive reactive network power demand can be calculated from the sum of the highest permissible individual active power P_(ref), P_(n) of the range A, divided by the number of active-power steps per power flow direction and a-c network (noting the minus sign for inductive values) can be summed for the networks N2, N2a, N2b and divided by 3. The respective values for Q_(NL) max, Q_(NC) max ; Q_(NL) mean and Q_(NC) mean (for the a-c networks N2, N2a, N2b in common) are entered into the Tables Ia to IVa.

Into the Tables Ib, c to IVb, c, the largest and smallest values of the reactive converter power, Q_(V) for the different a-c networks and power flow directions in the d-c-tie under favorable and unfavorable a-c network conditions are entered which are calculated in the manner discussed below.

Under favorable a-c network conditions, the minimum values Q_(V) with the highest permissible network voltage for the respective active power P_(ref), the corresponding reactive a-c network demand Q_(N) and all inductive compensation elements L are calculated. In this case, the action of the reactors is aided by the respective a-c network.

The maximum values Q_(V) on the other hand are determined with the smallest permissible network voltage for the respective active power P_(ref) (P_(n)), the corresponding a-c network reactive-power demand Q_(N) and all capacitive compensation elements C.

Under unfavorable a-c network conditions, the inner upper limit of Q_(V) over of each a-c network with the maximally permissible network voltage is calculated for the corresponding active power P_(ref), the corresponding reactive power demands Q_(N) and all associated capacitive compensation elements.

The inner lower limit Q_(V) under of each a-c network is calculated with the minimally permissible respective network voltage (range A) for the respective active power P_(ref), the corresponding Q_(N) and all inductive compensation elements provided.

The reactive-power demand Q_(N) of the a-c network must be covered by the capacitors as well as the filter circuits FK to the extent that Q_(V) is within the operating range.

For determining the required minimum and maximum transformation ratio u of the converter transformers T1, T2 and for checking existing converter transformers for applicability (Table XII), use is made of the equations ##EQU9## as well as ##EQU10## with

    U.sub.Nmin =U.sub.Nn ·0.85 and U.sub.Nmax =U.sub.Nn ·1.05

(where 0.85 is a value lower than the normal operation data).

The currents on the primary side of the converter transformers are obtained as ##EQU11## From this, the required reactive converter powers

    Q.sub.Vmin =√3·U.sub.Nn ·S.sub.iVmin ·sin γ.sub.min                                           (14)

    Q.sub.Vn =√3 U.sub.Nn ·S.sub.iVn ·sin α.sub.n                                             (15)

and, from the difference

    Q.sub.Vn -Q.sub.Vmin =ΔQ.sub.V,                      (16)

the reactive power excursion ΔQ_(V) of the converter transformers can be determined.

The reactive power demand of the cooperating two a-c networks must be compensated to the extent that the reactive converter powers for both sides are within the operating range, and therefor their difference is smaller than ΔQ_(V). By appropriate combination of the taps of the two converter transformers, a mutual approximation of the reactive converter power can then be accomplished.

The transmission of lowest converter d-c currents I_(d) and thereby minimizing of the transmission losses of the d-c-tie is achieved if the reactive power of both converters UR1, UR2 are at the lower limit of the respective operating range. So the limits of the operating range are given. The compensation elements are therefor determined as

    Q.sub.Vn =±1/2ΔQ.sub.v                            (17)

where Q_(Vn) =Q_(Vref), and form the desired operating range for the converter transformers used and the given voltage ranges A.

For converter transformers with:

    ______________________________________                                         a nominal short-circuit voltage                                                                      u.sub.Kn = 0.17                                          nominal converter d-c voltage                                                                        U.sub.dn = 24.4 kV                                       nominal control angle αn = 30°                                    extinction angle      γmin = 18°                                  one obtains  Q.sub.Vmin = 65 MVAr                                                           Q.sub.Vn = 115 MVAr = Q.sub.Vref                                               ΔQ.sub.V = 50 MVAr                                          ______________________________________                                    

and therefrom the underlimit 90 MVar and the upper limit 740 Mvar of operating range is decided in accordance with Q_(Vn) ±1/2ΔQ_(V).

From a comparison of the values Q_(NLmax) and Q_(NCmax) as well as Q_(NLmean), Q_(NCmean) for the a-c network N1 from Table Ia and corresponding values for the a-c network N2b from Table IVa, with Q_(V), the following compensation units are available for the networks N1 and N2, N2a, N2b.

For the network N1:

    Q.sub.NLmax +Q.sub.FK -Q.sub.Vref -Q.sub.indmax =69 (L) MVAr

    Q.sub.NCmax -Q.sub.FK +Q.sub.Vref -Q.sub.capmax =69 (C) MVAr

    Q.sub.NLmean +Q.sub.FK +Q.sub.Vref ↑Q.sub.indmean =42.6 (L) MVAr

    Q.sub.NCmean -Q.sub.FK +Q.sub.Vref =Q.sub.capmean =37.6 (C) MVAr

For the a-c network N1, Q_(L) =70 MVAr and Q_(C) =35 MVAr are sufficient, where Q_(L) is subdivided into two units of 35 MVAr each so that it is smaller than ΔQ_(V) =50 MVAr.

A similar consideration for the a-c networks N2, N2a, N2b yields three capacitors with 35 MVAr each as well as a choke with 35 MVAr, i.e., for both a-c networks N1, N2 (N2a, N2b) applies:

C₁ =35 MVAr, L₁₁ and L₁₂ are 35 MVAr each;

C₂₁, C₂₂, C₂₃ are 35 MVAr and L₂ each likewise 35 MVAr.

From the quantities Q_(FK), Q_(N), Q_(L), Q_(C) result the values Q_(V) contained in Tables Ib, c to IVb, c for the corresponding highest and smallest voltages of the respective ranges A according to the equations:

    Q.sub.V =Q.sub.FK +Q.sub.NL +Q.sub.C -Q.sub.L              (18)

and

    Q.sub.V =Q.sub.FK -Q.sub.NC +Q.sub.C -Q.sub.L, respectively, (19)

and more specifically referred to the respective p.u. voltages.

The calculated values in Tables Ib, c to IVb, c are presented in Tables V to X in such a way that for the individual a-c networks N1, N2; N2a, N2b, common regions are obtained from which, according to Table XI, common valid operating ranges for all a-c networks are taken which show that a common operating range exists for the d-c-tie determined according to the invention with reactive power control while maintaining a sufficient control reserve in the event of a-c network disturbances, dynamic processes of the a-c network and fast power changes of the generators in the a-c networks (power ramps) is assured with the converter transformers used and the compensation elements selected.

The values contained in the above-mentioned Table XI show that the operating range 90 to 140 MVAr can be started up with the determined compensation elements.

In the foregoing specification, the invention has been described with reference to specific exemplary embodiments thereof. It will, however, be evident that various modifications and changes may be made thereunto without departing from the broader spirit and scope of the invention as set forth in the appended claims. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense.

                                      TABLE I                                      __________________________________________________________________________     Network N1                                                                     RANGE A Powerflow direction N1 to N2                                                                      Powerflow direction N2 to N1                        Voltage P (MW)             P (MW)                                              in p.u. 200                                                                               150 100 50 20 0  20 50 100                                                                               150                                                                               200                                    __________________________________________________________________________     1,05  Q.sub.N                                                                          B  59 C                                                                               49 C                                                                               42 C                                                                              37 C  34 C                                                                              33 C                                                                              31 C                                                                              29 C                                                                              B  (a)                                 1,025 Q.sub.N                                                                          1 C        28 L                                                                              31,5 L                                                                               35 L                                                                              36 L     39 L                                   1,016 Q.sub.N  51 L                                                                               B  B     B  B  66 L                                         1,01  Q.sub.N                                                                             53 L                                                                               B   B  B     B  B  B  79 L                                                                              79 L                                   1,0   Q.sub.N                                                                          68 L                                                                              B   B   B  B     B  B  B  B  B                                      __________________________________________________________________________             Q.sub.NLmax = 79 MVAr                                                                            Q.sub.NLmean = 52,6 MVAr                                     Q.sub.NCmax = 59 MVAr                                                                            Q.sub.NCmean = 27,6 MVAr                             __________________________________________________________________________     1,05  Q.sub.V                                                                          B  95,4                                                                               105,4                                                                              112,4                                                                             117,4 120,4                                                                             121,4                                                                             123,4                                                                             125,4 (b)                                 1,025 Q.sub.V                                                                          146,1      175,1                                                                             178,6 182,1                                                                             183,1    186,1                                  1,016 Q.sub.V  195,5                                                                              B  B     B  B  210,5                                        1,01  Q.sub.V                                                                             195,8                                                                              B   B  B     B  B  B  221,8                                                                             221,8                                  1,0   Q.sub.V                                                                          208,0                                                                             B   B   B  B     B  B  B  B  B                                      1,05  Q.sub.V                                                                          B  -20,4                                                                              -10,4                                                                              -3,4                                                                              1,6   4,6                                                                               5,6                                                                               7,6                                                                               9,6                                                                               B  (c)                                 1,025 Q.sub.V                                                                          35,8       64,8                                                                              68,3  71,8                                                                              72,8     75,8                                   1,016 Q.sub.V  87,13                                                                              B  B     B  B  102,1                                        1,01  Q.sub.V                                                                             88,7                                                                               B   B  B     B  B  B  114,7                                                                             114,7                                  1,0   Q.sub.V                                                                          103,0                                                                             B   B   B  B     B  B  B  B  B                                      __________________________________________________________________________

                                      TABLE II                                     __________________________________________________________________________     Network N2                                                                     RANGE A Powerflow direction N1 to N2                                                                    Powerflow direction N2 to N1                          Voltage P (MW)           P (MW)                                                in p.u. 200                                                                               150                                                                               100                                                                               50 20 0  20 50  100 150 200                                   __________________________________________________________________________     1,05  Q.sub.N                                                                          51 C                                                                              54 C                                                                              57 C                                                                              65 C                                                                              71 C  77 C                                                                              87 C                                                                               100 C                                                                              118 C                                                                              B   (a)                               1,025 Q.sub.N                                                                          22 C                                                                              25 C                                                                              27 C                                                                              34 C                                                                              40 C  46 C                                                                              55 C                                                                               68 C                                                                               85 C                                                                               103 C                                 1,0   Q.sub.N                                                                          7 L                                                                               5 L                                                                               3 L                                                                               4 C                                                                               9 C   14 C                                                                              24 C                                                                               36 C                                                                               54 C                                                                               71 C                                  __________________________________________________________________________                       Q.sub.NLmax = 7 MVAr                                                           Q.sub.NCmax = 118 MVAr                                       __________________________________________________________________________     1,05  Q.sub.V                                                                          180,5                                                                             177,5                                                                             174,5                                                                             166,5                                                                             160,5 154,5                                                                             144,5                                                                              131,5                                                                              113,5                                                                              B   (b)                               1,025 Q.sub.V                                                                          198,6                                                                             195,6                                                                             193,6                                                                             186,6                                                                             180,6 174,6                                                                             165,6                                                                              152,6                                                                              135,6                                                                              117,6                                 1,0   Q.sub.V                                                                          217,0                                                                             215,0                                                                             213,0                                                                             206,0                                                                             201,0 196,0                                                                             186,0                                                                              174,0                                                                              156,0                                                                              139,0                                 1,05  Q.sub.V                                                                          26,2                                                                              23,2                                                                              20,2                                                                              12,2                                                                              6,2   0,2                                                                               -9,8                                                                               -22,8                                                                              -40,8                                                                              B   (c)                               1,025 Q.sub.V                                                                          51,5                                                                              48,5                                                                              46,5                                                                              39,5                                                                              33,5  27,5                                                                              18,5                                                                               5,5 -11,5                                                                              -29,5                                 1,0   Q.sub.V                                                                          77,0                                                                              75,0                                                                              73,0                                                                              66,0                                                                              61,0  56,0                                                                              46,0                                                                               34,0                                                                               16,0                                                                               -1,0                                  __________________________________________________________________________

                                      TABLE III                                    __________________________________________________________________________     Network N2a                                                                    RANGE A Powerflow direction N1 to N2a                                                                   Powerflow direction N2a to N1                         Voltage P (MW)           P (MW)                                                in p.u. 200                                                                               150                                                                               100                                                                               50 20 0  20 50 100                                                                               150                                                                               200                                      __________________________________________________________________________     1,05  Q.sub.N                                                                          9 C                                                                               12 C                                                                              17 C                                                                              24 C                                                                              28 C  33 C                                                                              39 C                                                                              50 C                                                                              B  B  (a)                                   1,025 Q.sub.N                                                                          36 L                                                                              33 L                                                                              28 L                                                                              22 L                                                                              18 L  12 L                                                                              6 L                                                                               5 C                                                                               17 C                                                                              30 C                                     1,0   Q.sub.N                                                                          80 L                                                                              77 L                                                                              73 L                                                                              68 L                                                                              B     B  51 L                                                                              40 L                                                                              28 L                                                                              15 L                                     __________________________________________________________________________                       Q.sub.NLmax = 80 MVAr                                                          Q.sub.NCmax = 50 MVAr                                        __________________________________________________________________________     1,05  Q.sub.V                                                                          222,5                                                                             219,5                                                                             214,5                                                                             207,5                                                                             203,5 198,5                                                                             192,5                                                                             181,5                                                                             B  B  (b)                                   1,025 Q.sub.V                                                                          256,6                                                                             253,6                                                                             248,6                                                                             242,6                                                                             238,6 232,6                                                                             226,6                                                                             215,6                                                                             203,6                                                                             190,6                                    1,0   Q.sub.V                                                                          290,0                                                                             287,0                                                                             283,0                                                                             278,0                                                                             B     B  261,0                                                                             250,0                                                                             238,0                                                                             225,0                                    1,05  Q.sub.V                                                                          68,2                                                                              65,2                                                                              60,2                                                                              53,2                                                                              49,2  44,2                                                                              38,2                                                                              27,2                                                                              B  B  (c)                                   1,025 Q.sub.V                                                                          109,5                                                                             106,5                                                                             101,5                                                                             95,5                                                                              91,5  85,5                                                                              79,5                                                                              68,5                                                                              56,5                                                                              43,5                                     1,0   Q.sub.V                                                                          150,0                                                                             147,0                                                                             143,0                                                                             138,0                                                                             B     B  121,0                                                                             110,0                                                                             98,0                                                                              85,0                                     __________________________________________________________________________

                                      TABLE IV                                     __________________________________________________________________________     Network N2b                                                                    RANGE A Powerflow direction N1 to N2b                                                                   Powerflow direction N2b to N1                         Voltage P (MW)           P (MW)                                                in p.u. 200                                                                               150                                                                               100                                                                               50 20 0  20 50  100 150 200                                   __________________________________________________________________________     1,05  Q.sub.N                                                                          60 C                                                                              63 C                                                                              68 C                                                                              74 C                                                                              80 C  84 C                                                                              92 C                                                                               104 C                                                                              B   B   (a)                               1,025 Q.sub.N                                                                          12 C                                                                              15 C                                                                              19 C                                                                              25 C                                                                              30 C  35 C                                                                              42 C                                                                               54 C                                                                               67 C                                                                               81 C                                  1,0   Q.sub.N                                                                          36 L                                                                              33 L                                                                              30 L                                                                              25 L                                                                              B     B  8 L 3 C 15 C                                                                               29 C                                  __________________________________________________________________________      Q.sub.NLmax =  Q.sub.NLmean =  9,5 MVAr                                                                      for all Networks N2,                            Q.sub.NCmax = 104 MVAr                                                                        Q.sub.NCmean = 60,5 MVAr                                                                      N2a, N2b together                                __________________________________________________________________________     1,05  Q.sub.V                                                                          171,5                                                                             168,5                                                                             163,5                                                                             157,5                                                                             151,5 147,5                                                                             139,5                                                                              127,5                                                                              B   B   (b)                               1,025 Q.sub.V                                                                          208,6                                                                             205,6                                                                             201,6                                                                             195,6                                                                             190,6 185,6                                                                             178,6                                                                              166,6                                                                              153,6                                                                              139,6                                 1,0   Q.sub.V                                                                          246,0                                                                             243,0                                                                             240,0                                                                             235,0                                                                             B     B  218,0                                                                              207,0                                                                              195,0                                                                              181,0                                 1,05  Q.sub.V                                                                          17,2                                                                              14,2                                                                              9,2                                                                               3,2                                                                               -2,8  -6,8                                                                              -14,8                                                                              -26,8                                                                              B   B   (c)                               1,025 Q.sub.V                                                                          61,5                                                                              58,5                                                                              54,5                                                                              48,5                                                                              43,5  38,5                                                                              31,5                                                                               19,5                                                                               6,5 -7,5                                  1,0   Q.sub.V                                                                          106,0                                                                             103,0                                                                             100,0                                                                             95,0                                                                              B     B  78,0                                                                               67,0                                                                               55,0                                                                               41,0                                  __________________________________________________________________________

                  TABLE V                                                          ______________________________________                                         Powerflow direction N1 to N2                                                                    Common region under                                                                  unfavorable                                                                               favorable                                                           Network    Network                                               N1    N2      conditions conditions                                   ______________________________________                                         200 MW Q.sub.Vmax                                                                             208,0   217,0 103,0-146,1                                                                             35,8-208,0                               P.sub.n                                                                               Q.sub.Vover                                                                            146,1   180,5                                                          Q.sub.Vunder                                                                           103,0    77,0                                                          Q.sub.Vmin                                                                              35,8    26,2                                                   150 MW Q.sub.Vmax                                                                             195,8   215,0 88,7-95,4                                                                               23,2-195,8                               P.sub.Ref                                                                             Q.sub.Vover                                                                             95,4   177,5                                                          Q.sub.Vunder                                                                            88,7    75,0                                                          Q.sub.Vmin                                                                             -20,4    23,2                                                   100 MW Q.sub.Vmax                                                                             195,5   213,0 87,1-105,4                                                                              20,2-195,5                               P.sub.Ref                                                                             Q.sub.Vover                                                                            105,4   174,5                                                          Q.sub.Vunder                                                                            87,1    73,0                                                          Q.sub.min                                                                              -10,4    20,2                                                    50 MW Q.sub.Vmax                                                                             175,1   206,0 66,0-112,4                                                                              12,2-175,1                               P.sub.Ref                                                                             Q.sub.Vover                                                                            112,4   166,5                                                          Q.sub.Vunder                                                                            64,8    66,0                                                          Q.sub.Vmin                                                                             -3,4     12,2                                                    20 MW Q.sub.Vmax                                                                             178,6   201,0 68,3-117,4                                                                               6,2-178,6                               P.sub.Ref                                                                             Q.sub.Vover                                                                            117,4   160,5                                                          Q.sub.Vunder                                                                            68,3    61,0                                                          Q.sub.Vmin                                                                              1,6     6,2                                                    ______________________________________                                    

                  TABLE VI                                                         ______________________________________                                         Powerflow direction N2 to N1                                                                    Common region under                                                                  unfavorable                                                                               favorable                                                           Network    Network                                               N1    N2      conditions conditions                                   ______________________________________                                         200 MW Q.sub.Vmax                                                                             221,8   139,0 114,7-117,6                                                                             75,8-139,0                               P.sub.n                                                                               Q.sub.Vover                                                                            186,1   117,6                                                          Q.sub.Vunder                                                                           114,7   -1,0                                                           Q.sub.Vmin                                                                              75,8   -29,5                                                   150 MW Q.sub.Vmax                                                                             221,8   156,0 113,5-114,7                                                                             9,6-156,0                                P.sub.Ref                                                                             Q.sub.Vover                                                                            125,4   113,5                                                          Q.sub.Vunder                                                                           114,7    16,0                                                          Q.sub.Vmin                                                                              9,6    -40,8                                                   100 MW Q.sub.Vmax                                                                             210,5   174,0 102,1-123,4                                                                             7,6-174,0                                P.sub.Ref                                                                             Q.sub.Vover                                                                            123,4   131,5                                                          Q.sub.Vunder                                                                           102,1    34,0                                                          Q.sub.min                                                                               7,6    -22,8                                                    50 MW Q.sub.Vmax                                                                             183,1   186,0  72,8-121,4                                                                             5,6-183,1                                P.sub.Ref                                                                             Q.sub.Vover                                                                            121,4   144,5                                                          Q.sub.Vunder                                                                            72,8    46,0                                                          Q.sub.Vmin                                                                              5,6    -9,8                                                     20 MW Q.sub.Vmax                                                                             182,1   196,0  71,8-120,4                                                                             4,6-182,1                                P.sub.Ref                                                                             Q.sub.Vover                                                                            120,4   154,5                                                          Q.sub.Vunder                                                                            71,8    56,0                                                          Q.sub.Vmin                                                                              4,6     0,2                                                    ______________________________________                                    

                  TABLE VII                                                        ______________________________________                                         Powerflow direction N1 to N2a                                                                   Common region under                                                                  unfavorable                                                                               favorable                                                           Network    Network                                               N1    N2a     conditions conditions                                   ______________________________________                                         200 MW Q.sub.Vmax                                                                             208,0   290,0 146,1-150,0                                                                             68,2-208,0                               P.sub.n                                                                               Q.sub.Vover                                                                            146,1   222,5                                                          Q.sub.Vunder                                                                           103,0   150,0                                                          Q.sub.Vmin                                                                              35,8    68,2                                                   150 MW Q.sub.Vmax                                                                             195,8   287,0  95,4-147,0                                                                             65,2-195,8                               P.sub.Ref                                                                             Q.sub.Vover                                                                             95,4   219,5                                                          Q.sub.Vunder                                                                            88,7   147,0                                                          Q.sub.Vmin                                                                             -20,4    65,2                                                   100 MW Q.sub.Vmax                                                                             195,5   283,0 105,4-143,0                                                                             60,2-195,5                               P.sub.Ref                                                                             Q.sub.Vover                                                                            105,4   214,7                                                          Q.sub.Vunder                                                                            87,1   143,0                                                          Q.sub.min                                                                              -10,4    60,2                                                    50 MW Q.sub.Vmax                                                                             175,1   278,0 112,4-138,0                                                                             53,2-175,1                               P.sub.Ref                                                                             Q.sub.Vover                                                                            112,4   207,5                                                          Q.sub.Vunder                                                                            64,8   138,0                                                          Q.sub.Vmin                                                                             -3,4     53,2                                                    20 MW Q.sub.Vmax                                                                             178,6   238,6  91,5-117,4                                                                             49,2-178,6                               P.sub.Ref                                                                             Q.sub.Vover                                                                            117,4   203,5                                                          Q.sub.Vunder                                                                            68,3    91,5                                                          Q.sub.Vmin                                                                              1,6     49,2                                                   ______________________________________                                    

                  TABLE VIII                                                       ______________________________________                                         Powerflow direction N2a to N1                                                                   Common Region under                                                                  unfavorable                                                                               favorable                                                           Network    Network                                               N1    N2a     conditions conditions                                   ______________________________________                                         200 MW Q.sub.Vmax                                                                             221,8   225,0 114,7-186,1                                                                             75,8-221,8                               P.sub.n                                                                               Q.sub.Vover                                                                            186,1   190,6                                                          Q.sub.Vunder                                                                           114,7    85,0                                                          Q.sub.Vmin                                                                              75,8    43,5                                                   150 MW Q.sub.Vmax                                                                             221,8   238,0 114,7-125,4                                                                             56,5-221,8                               P.sub.Ref                                                                             Q.sub.Vover                                                                            125,4   203,6                                                          Q.sub.Vunder                                                                           114,7    98,0                                                          Q.sub.Vmin                                                                              9,6     56,5                                                   100 MW Q.sub.Vmax                                                                             210,5   250,0 110,0-123,4                                                                             27,2-210,5                               P.sub.Ref                                                                             Q.sub.Vover                                                                            123,4   181,5                                                          Q.sub.Vunder                                                                           102,1   110,0                                                          Q.sub.min                                                                               7,6     27,2                                                    50 MW Q.sub.Vmax                                                                             183,1   261,0 121,0-121,4                                                                             38,2-183,1                               P.sub.Ref                                                                             Q.sub.Vover                                                                            121,4   192,5                                                          Q.sub.Vunder                                                                            72,8   121,0                                                          Q.sub.Vmin                                                                              5,6     38,2                                                    20 MW Q.sub.Vmax                                                                             182,1   232,6  85,5-120,4                                                                             44,2-182,1                               P.sub.Ref                                                                             Q.sub.Vover                                                                            120,4   198,5                                                          Q.sub.Vunder                                                                            71,8    85,5                                                          Q.sub.Vmin                                                                              4,6     44,2                                                   ______________________________________                                    

                  TABLE IX                                                         ______________________________________                                         Powerflow direction N1 to N2b                                                                   Common Region under                                                                  unfavorable                                                                               favorable                                                           Network    Network                                               N1    N2b     conditions conditions                                   ______________________________________                                         200 MW Q.sub.Vmax                                                                             208,0   246,0 106,0-146,1                                                                             35,8-208,0                               P.sub.n                                                                               Q.sub.Vover                                                                            146,1   171,5                                                          Q.sub.Vunder                                                                           103,0   106,0                                                          Q.sub.Vmin                                                                              35,8    17,2                                                   150 MW Q.sub.Vmax                                                                             195,8   243,0  95,4-103,0                                                                             14,2-195,8                               P.sub.Ref                                                                             Q.sub.Vover                                                                             95,4   168,5                                                          Q.sub.Vunder                                                                            88,7   103,0                                                          Q.sub.Vmin                                                                             -20,4    14,2                                                   100 MW Q.sub.Vmax                                                                             195,5   240,0 100,0-105,4                                                                             9,2-195,5                                P.sub.Ref                                                                             Q.sub.Vover                                                                            105,4   163,5                                                          Q.sub.Vunder                                                                            87,1   100,0                                                          Q.sub.min                                                                              -10,4    9,2                                                     50 MW Q.sub.Vmax                                                                             175,1   235,0  95,0-112,4                                                                             3,2-175,1                                P.sub.Ref                                                                             Q.sub.Vover                                                                            112,4   157,5                                                          Q.sub.Vunder                                                                            64,8    95,0                                                          Q.sub.Vmin                                                                             -3,4     3,2                                                     20 MW Q.sub.Vmax                                                                             178,6   190,6  68,3-117,4                                                                             1,6-178,6                                P.sub.Ref                                                                             Q.sub.Vover                                                                            117,4   151,5                                                          Q.sub.Vunder                                                                            68,3    43,5                                                          Q.sub.Vmin                                                                              1,6    -2,8                                                    ______________________________________                                    

                  TABLE X                                                          ______________________________________                                         Powerflow direction N2b to N1                                                                   Common Region under                                                                  unfavorable                                                                               favorable                                                           Network    Network                                               N1    N2b     conditions conditions                                   ______________________________________                                         200 MW Q.sub.Vmax                                                                             221,8   181,0 114,7-139,6                                                                             75,8-181,0                               P.sub.n                                                                               Q.sub.Vover                                                                            186,1   139,6                                                          Q.sub.Vunder                                                                           114,7    41,0                                                          Q.sub.Vmin                                                                              75,8   -7,5                                                    150 MW Q.sub.Vmax                                                                             221,8   195,0 114,7-125,4                                                                             9,6-195,0                                P.sub.Ref                                                                             Q.sub.Vover                                                                            125,4   153,6                                                          Q.sub.Vunder                                                                           114,7    55,0                                                          Q.sub.Vmin                                                                              9,6     6,5                                                    100 MW Q.sub.Vmax                                                                             210,5   207,0 102,1-123,4                                                                             7,6-207,0                                P.sub.Ref                                                                             Q.sub.Vover                                                                            123,4   127,5                                                          Q.sub.Vunder                                                                           102,1    67,0                                                          Q.sub.Vmin                                                                              7,6    -26,8                                                    50 MW Q.sub.Vmax                                                                             183,1   218,0  78,0-121,4                                                                             5,6-218,0                                P.sub.Ref                                                                             Q.sub.Vover                                                                            121,4   139,5                                                          Q.sub.Vunder                                                                            72,8    78,0                                                          Q.sub.Vmin                                                                              5,6    -14,8                                                    20 MW Q.sub.Vmax                                                                             182,1   185,6  71,8-120,4                                                                             4,6-182,1                                P.sub.Ref                                                                             Q.sub.Vover                                                                            120,4   147,5                                                          Q.sub.Vunder                                                                            71,8    38,5                                                          Q.sub.Vmin                                                                              4,6    -6,8                                                    ______________________________________                                    

                  TABLE XI                                                         ______________________________________                                         Largest common operating region of the reactive                                converter power of all a-c-networks                                                    under favorable                                                                             under unfavorable                                                 Network conditions                                                                          Network conditions                                        ______________________________________                                         P =  200 MW   75,8 to 139,0 MVAr                                                                              103,0 to                                                                              139,0 MVAr                                    150 MW   65,2    156,0 MVAr                                                                               88,7  147,0 MVAr                                    100 MW   60,2    174,0 MVAr                                                                               87,1  143,0 MVAr                                     50 MW   53,2    175,1 MVAr                                                                               66,0  138,0 MVAr                                     20 MW   49,2    178,6 MVAr                                                                               68,3  120,4 MVAr                               ______________________________________                                    

                  TABLE XII                                                        ______________________________________                                         Data of the converter transformers of the d-c-tie                                                     Short                                                                 max. per-                                                                               circuit                                                 Voltage limits for the                                                                       missible voltage transformation                                  bus bar voltage                                                                              tap      U.sub.Kn                                                                               ratio                                           ______________________________________                                         smaller to                                                                             209,29 kV 35       0,1530                                                                               0,110449                                                                              u.sub.max                              209,3   213,89    34       0,1550                                                                               0,108696                                      213,9   216,19    33       0,1560                                                                               0,106997                                      216,2   220,79    32       0,1580                                                                               0,105351                                      220,8   223,09    31       0,1590                                                                               0,103755                                      223,1   227,69    30       0,1600                                                                               0,102206                                      227,7   229,99    29       0,1610                                                                               0,100703                                      230,0   234,59    28       0,1620                                                                               0,099244                                      234,6   236,89    27       0,1630                                                                               0,097826                                      236,9   241,49    26       0,1650                                                                               0,096448                                      241,5   243,79    25       0,1660                                                                               0,095109                                      243,8   248,39    24       0,1670                                                                               0,093806                                      248,4   250,69    23       0,1690                                                                               0,092538                                      250,7   greater   22       0,1700                                                                               0,091304                                                                              nominal value                                            21       0,1720                                                                               0,090103                                                        20       0,1730                                                                               0,088933                                                        19       0,1740                                                                               0,087793                                                        18       0,1720                                                                               0,086681                                                        17       0,1730                                                                               0,085598                                                        16       0,1740                                                                               0,08541                                                         15       0,1760                                                                               0,083510                                                        14       0,1770                                                                               0,082504                                                                              u.sub.min                                                13       0,1780                                                                               0,081522                                                        12       0,1790                                                                               0,080563                                                        11       0,1800                                                                               0,796626                                                        10       0,1810                                                                               0,078711                                                        9        0,1830                                                                               0,077816                                                        8        0,1840                                                                               0,076942                                                        7        0,1850                                                                               0,076087                                                        6        0,1860                                                                               0,075251                                                        5        0,1870                                                                               0,074433                                                        4        0,1880                                                                               0,073633                                                        3        0,1900                                                                               0,072849                                                        2        0,1910                                                                               0,072082                                                        1        0,1920                                                                               0,071332                                      ______________________________________                                     

We claim:
 1. A combined power and a-c voltage control method for a d-c high-voltage transmission system (d-c-tie) connecting two three-phase a-c networks by a connecting point with influencing of the reactive-power of both a-c networks by at least one of a shunt reactor and a capacitor and further having a converter and a converter transformer for each network, the converter transformer being switchable by a tap changer for maintaining a voltage of the a-c networks on the connecting point of the d-c-tie, the method comprising the steps of switching tap positions of both converter transformers to perform simultaneous active and reactive power control of both a-c networks by combinations of selected ones of fixed and switchable shunt capacitors and shunt reactors comprising compensation means, further including setting the tap changer of both converter transformers to obtain an optimum operating point for the converters of the d-c-tie at a maximally permissible tap position for the respective operating voltage of one converter transformer, the converter transformers each having a primary connected to the network and a secondary connected to the d-c tie and wherein a ratio of the primary currents of the two converter transformers and a transformation ratio of the maximally permissible tap position of the one converter transformer to a tap position of the other converter transformer is chosen in accordance with the relationship ##EQU12## taking into consideration a relationship defining a prevailing d-c current in the d-c tie ##EQU13## to obtain a permissible d-c current I_(dmin) for the d-c-tie meeting all a-c network requirements, equal to one-half of the sum of the theoretical d-c currents of both converters, wherein u₁, u₂ are the converter transformer transformation ratios; S_(iV1), S_(iV2) are the primary currents of the converter transformers; b is a number of the series-connected converter bridges in the converters; ρ₁, ρ₂, χ₂, χ₁ are variables dependent on control angles α, extinction angles γ, and overlap angles u in accordance with the following equations: ##EQU14##
 2. The control method recited in claim 1, wherein the optimum operating points for the converters of the d-c-tie connected to both a-c networks are located within a region which is determined by the number of shunt reactors or capacitors provided, and the size of the respective converter transformers, the number and magnitude of the tap changer positions and the voltage-dependent reactive-power demands of the a-c networks.
 3. The control method recited in claim 1, wherein, for supporting one a-c network, the d-c current determined for the converter connected to said one a-c network is set as a transmission current.
 4. The control method recited in claim 1, wherein maximum and minimum transformation ratios u_(max), u_(min) of the converter transformers are designed as a function of a nominal d-c voltage U_(dn) of the converters, a network voltage U_(N), a nominal transformer short circuit voltage u_(Kn), a nominal control angle α_(n) and an extinction angle γ min responsible for the power flow in both directions according to the relations: ##EQU15##
 5. The control method recited in claim 2, wherein from reactive powers Q_(Vn) equal to Q_(Vref) at a nominal control angle α_(n) and Q_(Vmin) with an extinction angle γ_(min), the lower and upper limits of the operating range with the compensation means are determined by Q_(ref) =±1/2ΔQ_(V), where ΔQ_(V) is the difference between Q_(Vn) and Q_(Vmin), and wherein the converter transformers approach the operating point with minimum losses therefor and sufficient control reserves, maintaining the requirements set by a utility. 